| variable | shapiro_stat | p_value | skewness | kurtosis | n |
|---|---|---|---|---|---|
| butterfly_diff_sqrt | 0.9893 | 0.6368 | 0.2251 | -0.3143 | 96 |
| butterfly_diff_95th_sqrt | 0.9880 | 0.5411 | 0.0120 | -0.6497 | 96 |
| butterfly_diff_top3_sqrt | 0.9875 | 0.5027 | 0.0266 | -0.6207 | 96 |
| butterfly_diff_95th | 0.9182 | 0.0000 | -0.3705 | 2.0466 | 96 |
| butterfly_diff_top3 | 0.9126 | 0.0000 | -0.0126 | 2.4706 | 96 |
| butterfly_diff | 0.8835 | 0.0000 | 0.3794 | 4.3938 | 96 |
| butterfly_diff_95th_sq | 0.6591 | 0.0000 | -1.2037 | 9.1440 | 96 |
| butterfly_diff_top3_sq | 0.6327 | 0.0000 | 0.6220 | 10.0799 | 96 |
| butterfly_diff_sq | 0.5307 | 0.0000 | 1.9996 | 19.7056 | 96 |
Dynamic Window GAM Analysis: Comprehensive Synthesis
0.1 Background
This document synthesizes results from two parallel GAM analyses investigating the relationship between weather conditions and monarch butterfly roost abandonment. Both analyses address feedback from Francis regarding temporal alignment of weather predictors with butterfly responses.
The original daily-level analysis used fixed 6am-6pm weather windows, which Francis identified as having a temporal logic issue:
“All of the metrics for wind, temperature and light, would need to be re-calculated for 24 hour periods that begin at the time of the highest count.”
Francis’s key points:
- Temporal alignment: Butterflies can only respond to weather after it occurs
- Biological timing: If max count occurred at 2pm on day t-1, the relevant weather window should start at 2pm, not 6am
- Roosting decisions: Weather from max count through sunset determines whether butterflies abandon the roost
0.2 Two-Window Comparison Approach
To address this feedback while exploring biological relevance, we conducted two parallel analyses:
Sunset Window Analysis (variable-length windows):
- Weather window:
time_of_max_count_t_1→last_observation_time_t(functional sunset) - Mean duration: 29.6 hours (range: 22.5-34.9 hours)
- Captures overnight conditions through sunset when roosting decisions finalize
- Tests: “Do conditions from peak count to sunset predict roost abandonment?”
- Data:
monarch_daily_lag_analysis_sunset_window.csv(n=103 lag pairs)
24-Hour Window Analysis (fixed-length windows):
- Weather window:
time_of_max_count_t_1→+24 hours - Fixed duration: exactly 24 hours for all observations
- Standardized exposure period following peak count
- Tests: “Do conditions in 24 hours following peak count predict roost abandonment?”
- Data:
monarch_daily_lag_analysis_24hr_window.csv(n=94 lag pairs)
Both analyses use identical modeling approaches to enable direct comparison of results across window definitions.
1 Response Variable Selection
We evaluated three butterfly difference metrics (max, 95th percentile, and top 3 mean) with three transformations each (untransformed, square root, and square) to determine which best approximates normality for GAM modeling.
1.1 Normality Testing Results
1.2 Selected Response Variable
butterfly_diff_sqrt was selected as the response variable for both analyses based on having the highest Shapiro-Wilk W statistic, indicating best approximation to normality.
This represents the square root transformation of the change in maximum butterfly count from day t-1 to day t. The transformation:
2 Candidate Predictor Variables
A total of 19 candidate predictors (3 baseline butterfly metrics + 16 weather/window metrics) were calculated within each observation’s dynamic window:
| Variable | Category | Description |
|---|---|---|
| max_butterflies_t_1 | Baseline | Maximum butterfly count on previous day |
| butterflies_95th_percentile_t_1 | Baseline | 95th percentile count on previous day |
| butterflies_top3_mean_t_1 | Baseline | Mean of top 3 counts on previous day |
| temp_min | Temperature | Minimum temperature in lag window |
| temp_max | Temperature | Maximum temperature in lag window |
| temp_mean | Temperature | Mean temperature in lag window |
| temp_at_max_count_t_1 | Temperature | Temperature at time of maximum count on t-1 |
| hours_above_15C | Temperature | Cumulative Hours ≥15°C in lag window |
| degree_hours_above_15C | Temperature | Cumulative degree-hours above 15°C |
| wind_avg_sustained | Wind | Mean sustained wind speed in lag window |
| wind_max_gust | Wind | Maximum wind gust in lag window |
| wind_gust_sum | Wind | Sum of all gust measurements in lag window |
| wind_gust_sum_above_2ms | Wind | Sum of gusts >2 m/s (threshold-based wind exposure) |
| wind_gust_hours | Wind | Gust-hours (integral approximation of wind exposure over time) |
| wind_minutes_above_2ms | Wind | Minutes with wind speed ≥2 m/s |
| wind_gust_sd | Wind | Standard deviation of gust speeds |
| wind_mode_gust | Wind | Most frequent gust speed (modal wind conditions) |
| sum_butterflies_direct_sun | Sun Exposure | Sum of butterflies observed in direct sunlight across entire lag window |
| lag_duration_hours | Window | Duration of lag window in hours. Used only for sunset analysis as a control variable. |
2.1 Full Correlation Matrix (All Candidates)
The full correlation matrix reveals substantial multicollinearity among candidate predictors, particularly within variable categories:
These patterns guided predictor selection to avoid multicollinearity issues.
2.2 Selected Predictors Correlation Matrix
Based on correlation structure, biological relevance, and variance inflation considerations, we selected 5 final predictors representing distinct aspects of weather exposure:
Final predictor set:
temp_min- Minimum temperaturetemp_max- Maximum temperaturetemp_at_max_count_t_1- Temperature at time of peak countwind_max_gust- Maximum wind gust, matching 30 minute analysissum_butterflies_direct_sun- Total minutes butterflies exposed to direct sun
2.2.1 Wind Gust Mode: An Excluded Variable
wind_gust_mode was initially considered as a candidate predictor due to its low correlation with other wind metrics (r < 0.3 with wind_max_gust). However, wind_gust_mode had to be excluded from model fitting due to having only 5 unique values across all observations. This extreme discretization caused model convergence issues.
3 Model Building Strategy
Both analyses employed an identical systematic model-building approach to ensure comparability.
3.1 Model Space Exploration
We fit 76 models spanning a hierarchy of complexity:
- Null models (2): Intercept only, with smooth vs. linear baseline
- Single predictor models (10): Each of 5 predictors, smooth vs. linear
- Interaction-only models (20): All 2-way interactions, smooth vs. linear
- Additive models (14): Multiple predictors without interactions, smooth vs. linear
- Main + Interaction models (20): Additive + selected interactions, smooth vs. linear
- Complex models (8): All temperatures, all temps + wind, etc.
- Full models (2): All predictors + all interactions, smooth vs. linear
This systematic exploration tests:
- Individual predictor effects: Which variables matter in isolation?
- Interaction effects: Do predictors combine synergistically?
- Functional form: Linear vs. smooth (spline) relationships?
- Model complexity: What level of complexity is justified by data?
3.2 GAM Structure
All models used the same core structure:
butterfly_diff_sqrt ~ predictors + s(deployment_id, bs="re")
+ correlation = corAR1(form = ~1|deployment_id)Key components:
- Response:
butterfly_diff_sqrt(square root transformed change in maximum count) - Random effects:
s(deployment_id, bs="re")accounts for repeated measures within deployments - Autocorrelation:
corAR1()models temporal autocorrelation within deployments - Functional form: Smooth terms
s()for nonlinear relationships vs. linear terms - Family: Gaussian with identity link (justified by normality of transformed response)
3.3 Overfitting Controls
To prevent overfitting with small sample sizes (n=94-103), we implemented:
- AICc (corrected AIC): Primary model selection criterion, penalizes parameters more heavily than AIC
- Degrees of freedom ratio: Tracked df/n ratio (flagged if >0.25)
- Observations per parameter: Monitored n/df (flagged if <5)
- Cross-validation: LOOCV to assess out-of-sample prediction error
- Overfitting risk classification: Models flagged as Low/Moderate/High risk based on df ratios
Models with df/n > 0.4 or obs/param < 3 were flagged as High overfitting risk.
3.4 Model Comparison Approach
Models were compared using:
- AICc ranking: Lower AICc indicates better balance of fit and complexity
- ΔAICc: Difference from best model (ΔAICc > 10 indicates substantially worse fit)
- AICc weights: Relative likelihood of each model being the best
- Cross-validation RMSE: Out-of-sample prediction error
- BIC: Alternative information criterion (more conservative penalty)
Selection criteria:
- Best model: Lowest AICc
- Competitive models: ΔAICc < 2
- Considerably worse: ΔAICc > 10
4 Sunset Window Analysis Results
4.1 Model Comparison
The table below shows the top 30 models ranked by AICc for the sunset window analysis:
| model | description | AICc | delta_AICc | weight_AICc | df | obs_per_param | overfitting_risk |
|---|---|---|---|---|---|---|---|
| M31 | Interaction: wind_max_gust × sum_butterflies_direct_sun (smooth) | 640.22 | 0.00 | 0.7993 | 11 | 8.73 | Low |
| M51 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (smooth) | 644.13 | 3.90 | 0.1135 | 15 | 6.40 | Low |
| M45 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (smooth) | 648.52 | 8.29 | 0.0126 | 15 | 6.40 | Low |
| M32 | Interaction: wind_max_gust × sum_butterflies_direct_sun (linear) | 648.85 | 8.63 | 0.0107 | 9 | 10.67 | Low |
| M19 | Interaction: temp_min × sum_butterflies_direct_sun (smooth) | 649.34 | 9.12 | 0.0084 | 11 | 8.73 | Low |
| M5 | Single: temp_max (smooth) | 649.46 | 9.23 | 0.0079 | 10 | 9.60 | Low |
| M29 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (smooth) | 649.74 | 9.52 | 0.0069 | 11 | 8.73 | Low |
| M43 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (smooth) | 650.12 | 9.89 | 0.0057 | 15 | 6.40 | Low |
| M23 | Interaction: temp_max × wind_max_gust (smooth) | 650.17 | 9.95 | 0.0055 | 11 | 8.73 | Low |
| M33 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (smooth) | 650.52 | 10.30 | 0.0046 | 15 | 6.40 | Low |
| M39 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (smooth) | 651.39 | 11.17 | 0.0030 | 15 | 6.40 | Low |
| M25 | Interaction: temp_max × sum_butterflies_direct_sun (smooth) | 651.78 | 11.56 | 0.0025 | 11 | 8.73 | Low |
| M59 | Additive: temp_max + wind_max_gust (smooth) | 652.14 | 11.92 | 0.0021 | 12 | 8.00 | Low |
| M55 | Additive: temp_min + temp_max (smooth) | 652.25 | 12.03 | 0.0020 | 12 | 8.00 | Low |
| M15 | Interaction: temp_min × temp_at_max_count_t_1 (smooth) | 652.64 | 12.42 | 0.0016 | 11 | 8.73 | Low |
| M17 | Interaction: temp_min × wind_max_gust (smooth) | 652.73 | 12.51 | 0.0015 | 11 | 8.73 | Low |
| M11 | Single: sum_butterflies_direct_sun (smooth) | 652.82 | 12.60 | 0.0015 | 10 | 9.60 | Low |
| M13 | Interaction: temp_min × temp_max (smooth) | 652.93 | 12.71 | 0.0014 | 11 | 8.73 | Low |
| M1 | Null (smooth baseline) | 653.17 | 12.95 | 0.0012 | 8 | 12.00 | Low |
| M21 | Interaction: temp_max × temp_at_max_count_t_1 (smooth) | 653.48 | 13.26 | 0.0011 | 11 | 8.73 | Low |
| M27 | Interaction: temp_at_max_count_t_1 × wind_max_gust (smooth) | 653.70 | 13.47 | 0.0009 | 11 | 8.73 | Low |
| M49 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (smooth) | 653.88 | 13.66 | 0.0009 | 15 | 6.40 | Low |
| M7 | Single: temp_at_max_count_t_1 (smooth) | 653.91 | 13.68 | 0.0009 | 10 | 9.60 | Low |
| M52 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (linear) | 654.45 | 14.23 | 0.0007 | 13 | 7.38 | Low |
| M41 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (smooth) | 654.72 | 14.50 | 0.0006 | 15 | 6.40 | Low |
| M3 | Single: temp_min (smooth) | 655.44 | 15.21 | 0.0004 | 10 | 9.60 | Low |
| M9 | Single: wind_max_gust (smooth) | 655.52 | 15.30 | 0.0004 | 10 | 9.60 | Low |
| M53 | Additive: All temperature (smooth) | 655.96 | 15.73 | 0.0003 | 14 | 6.86 | Low |
| M67 | All temp + all temp interactions (smooth) | 656.75 | 16.53 | 0.0002 | 23 | 4.17 | Moderate |
| M20 | Interaction: temp_min × sum_butterflies_direct_sun (linear) | 656.77 | 16.55 | 0.0002 | 9 | 10.67 | Low |
Best model: M31 - wind_max_gust × sum_butterflies_direct_sun (smooth interaction)
- AICc = 640.22
- ΔAICc = 0 (best model)
- AICc weight = 0.799 (79.9% probability of being best model)
- df = 11, obs/param = 8.7 (Low overfitting risk)
4.2 Cross-Validation Results
Cross-validation RMSE for top 5 models:See sunset_window_gam_analysis.html for detailed cross-validation results.The best model (M31) showed stable out-of-sample performance with RMSEcompetitive with or better than more complex models, supporting its selection.4.3 Best Model Summary
Model M31: wind_max_gust × sum_butterflies_direct_sun (smooth interaction only)
This simple interaction-only model outperformed all additive and complex models, suggesting the relationship between weather and butterfly roost abandonment is primarily driven by the synergistic effect of wind gusts and sun exposure.
Model equation:
butterfly_diff_sqrt ~ te(wind_max_gust, sum_butterflies_direct_sun)
+ s(deployment_id, bs="re")Interpretation:
The wind × sun interaction suggests that the effect of wind on roost abandonment depends on sun exposure, or vice versa. This could reflect:
- Butterflies more vulnerable to wind when actively foraging in sun
- Combined thermal and mechanical stress under high sun + high wind
- Behavioral responses differing based on environmental context
4.4 Partial Effects Plots
The interaction surface shows the predicted change in butterfly counts as a function of both wind gusts and sun exposure.
4.5 Model Diagnostics
Diagnostic assessment:
- Residuals vs. Fitted: No strong patterns, suggesting adequate model fit
- Q-Q Plot: Residuals approximately normal with some deviation in tails
- Scale-Location: Homoscedasticity appears reasonable
- Residuals vs. Leverage: No high-leverage outliers driving results
4.6 Autocorrelation Diagnostics
The ACF and PACF plots show residual autocorrelation structure after accounting for AR(1) correlation structure in the model.
4.7 GAM-Specific Diagnostics
Standard gam.check() diagnostics showing basis dimension adequacy and residual distribution.
5 24-Hour Window Analysis Results
5.1 Model Comparison
The table below shows the top 30 models ranked by AICc for the 24-hour window analysis:
| model | description | AICc | delta_AICc | weight_AICc | df | obs_per_param | overfitting_risk |
|---|---|---|---|---|---|---|---|
| M31 | Interaction: wind_max_gust × sum_butterflies_direct_sun (smooth) | 636.33 | 0.00 | 0.5073 | 9 | 10.44 | Low |
| M23 | Interaction: temp_max × wind_max_gust (smooth) | 639.92 | 3.59 | 0.0844 | 9 | 10.44 | Low |
| M29 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (smooth) | 640.76 | 4.42 | 0.0555 | 9 | 10.44 | Low |
| M19 | Interaction: temp_min × sum_butterflies_direct_sun (smooth) | 641.11 | 4.78 | 0.0466 | 9 | 10.44 | Low |
| M51 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (smooth) | 641.72 | 5.39 | 0.0342 | 13 | 7.23 | Low |
| M45 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (smooth) | 641.80 | 5.46 | 0.0330 | 13 | 7.23 | Low |
| M5 | Single: temp_max (smooth) | 642.19 | 5.86 | 0.0271 | 8 | 11.75 | Low |
| M67 | All temp + all temp interactions (smooth) | 642.49 | 6.16 | 0.0233 | 21 | 4.48 | Moderate |
| M43 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (smooth) | 642.69 | 6.36 | 0.0211 | 13 | 7.23 | Low |
| M17 | Interaction: temp_min × wind_max_gust (smooth) | 642.73 | 6.40 | 0.0207 | 9 | 10.44 | Low |
| M25 | Interaction: temp_max × sum_butterflies_direct_sun (smooth) | 642.75 | 6.42 | 0.0205 | 9 | 10.44 | Low |
| M33 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (smooth) | 642.90 | 6.57 | 0.0190 | 13 | 7.23 | Low |
| M41 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (smooth) | 643.73 | 7.40 | 0.0126 | 13 | 7.23 | Low |
| M15 | Interaction: temp_min × temp_at_max_count_t_1 (smooth) | 643.79 | 7.46 | 0.0122 | 9 | 10.44 | Low |
| M32 | Interaction: wind_max_gust × sum_butterflies_direct_sun (linear) | 644.33 | 8.00 | 0.0093 | 8 | 11.75 | Low |
| M53 | Additive: All temperature (smooth) | 644.61 | 8.28 | 0.0081 | 12 | 7.83 | Low |
| M27 | Interaction: temp_at_max_count_t_1 × wind_max_gust (smooth) | 644.95 | 8.62 | 0.0068 | 9 | 10.44 | Low |
| M59 | Additive: temp_max + wind_max_gust (smooth) | 645.02 | 8.69 | 0.0066 | 10 | 9.40 | Low |
| M55 | Additive: temp_min + temp_max (smooth) | 645.02 | 8.69 | 0.0066 | 10 | 9.40 | Low |
| M21 | Interaction: temp_max × temp_at_max_count_t_1 (smooth) | 645.52 | 9.19 | 0.0051 | 9 | 10.44 | Low |
| M1 | Null (smooth baseline) | 645.54 | 9.21 | 0.0051 | 6 | 15.67 | Low |
| M13 | Interaction: temp_min × temp_max (smooth) | 645.90 | 9.57 | 0.0042 | 9 | 10.44 | Low |
| M39 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (smooth) | 646.00 | 9.66 | 0.0040 | 13 | 7.23 | Low |
| M7 | Single: temp_at_max_count_t_1 (smooth) | 646.19 | 9.86 | 0.0037 | 8 | 11.75 | Low |
| M49 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (smooth) | 646.79 | 10.46 | 0.0027 | 13 | 7.23 | Low |
| M3 | Single: temp_min (smooth) | 647.30 | 10.97 | 0.0021 | 8 | 11.75 | Low |
| M24 | Interaction: temp_max × wind_max_gust (linear) | 647.38 | 11.05 | 0.0020 | 8 | 11.75 | Low |
| M9 | Single: wind_max_gust (smooth) | 647.82 | 11.49 | 0.0016 | 8 | 11.75 | Low |
| M11 | Single: sum_butterflies_direct_sun (smooth) | 648.02 | 11.69 | 0.0015 | 8 | 11.75 | Low |
| M30 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (linear) | 648.22 | 11.89 | 0.0013 | 8 | 11.75 | Low |
Best model: M31 - wind_max_gust × sum_butterflies_direct_sun (smooth interaction)
- AICc = 636.33
- ΔAICc = 0 (best model)
- AICc weight = 0.507 (50.7% probability of being best model)
- df = 9, obs/param = 10.4 (Low overfitting risk)
5.2 Cross-Validation Results
Cross-validation RMSE for top 5 models:See 24hr_window_gam_analysis.html for detailed cross-validation results.The best model (M31) showed stable out-of-sample performance consistentwith the sunset window analysis results.5.3 Best Model Summary
Model M31: wind_max_gust × sum_butterflies_direct_sun (smooth interaction only)
Remarkably, the identical model structure emerged as best for the 24-hour window, providing convergent evidence that the wind × sun interaction is the primary driver of roost abandonment across different window definitions.
Model equation:
butterfly_diff_sqrt ~ te(wind_max_gust, sum_butterflies_direct_sun)
+ s(deployment_id, bs="re")5.4 Partial Effects Plots
The interaction surface is qualitatively similar to the sunset window analysis, showing comparable patterns in how wind and sun combine to predict butterfly count changes.
5.5 Model Diagnostics
Diagnostic assessment:
- Residuals vs. Fitted: Reasonably homoscedastic with no strong patterns
- Q-Q Plot: Residuals approximately normal
- Scale-Location: Variance appears stable across fitted values
- Residuals vs. Leverage: No problematic outliers
5.6 Autocorrelation Diagnostics
ACF and PACF plots for the 24-hour window model residuals.
5.7 GAM-Specific Diagnostics
Standard GAM diagnostics showing adequate basis dimensions and reasonable residual behavior.
6 Window Comparison: Convergent Results
Both the sunset window (variable-length, ending at functional sunset) and 24-hour window (fixed-length, standardized duration) analyses yielded the same best model:
M31: wind_max_gust × sum_butterflies_direct_sun (smooth interaction)
This convergence provides strong evidence that the wind × sun interaction is robust across different temporal window definitions.
Key convergent findings:
- Same predictor combination: Wind gusts and sun exposure, with no main effects
- Same functional form: Smooth tensor product interaction (non-linear)
- Simple model structure: Interaction-only model beats all additive and complex alternatives
- Low overfitting risk: Both models have reasonable df/n ratios and obs/param values
- Robust across windows: Result holds for biologically-defined (sunset) and standardized (24hr) windows
Implications:
- The relationship between weather and roost abandonment is primarily context-dependent: neither wind nor sun alone predict abandonment, but their combination does
- The effect is nonlinear: simple additive models cannot capture the interaction
- The signal is robust: it emerges consistently despite differences in sample size (n=103 vs n=94) and window definition
7 Model Fitting Notes
7.1 Convergence
All 76 models (in both analyses) converged successfully with the following exceptions:
- Models including
wind_gust_modefailed to converge (variable excluded) - Full models (M71, M72) converged but flagged as high overfitting risk (df/n > 0.4)
7.2 Computational Details
- Software: R 4.x, mgcv package for GAM fitting
- Optimization: Outer iteration with GCV/REML for smoothness selection
- Basis dimensions: Default k values, checked via
gam.check() - AR1 correlation: Fitted via
gamm()using nlme correlation structures
7.3 Data Filtering
Both analyses filtered observations to:
metrics_complete >= 0.95(≥95% weather data completeness)- Complete cases for all 5 selected predictors
- Sunset window: n = 103 → 96 after filtering
- 24-hour window: n = 94 → 94 (no additional filtering)
8 Appendix: Full Model Comparison Tables
8.1 Sunset Window: All 76 Models
| model | description | AICc | delta_AICc | weight_AICc | baseline_type | model_category | overfitting_risk |
|---|---|---|---|---|---|---|---|
| M31 | Interaction: wind_max_gust × sum_butterflies_direct_sun (smooth) | 640.22 | 0.00 | 7.99e-01 | Smooth | Interaction only | Low |
| M51 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (smooth) | 644.13 | 3.90 | 1.13e-01 | Smooth | Main + Interaction | Low |
| M45 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (smooth) | 648.52 | 8.29 | 1.26e-02 | Smooth | Main + Interaction | Low |
| M32 | Interaction: wind_max_gust × sum_butterflies_direct_sun (linear) | 648.85 | 8.63 | 1.07e-02 | Linear | Interaction only | Low |
| M19 | Interaction: temp_min × sum_butterflies_direct_sun (smooth) | 649.34 | 9.12 | 8.36e-03 | Smooth | Interaction only | Low |
| M5 | Single: temp_max (smooth) | 649.46 | 9.23 | 7.90e-03 | Smooth | Single predictor | Low |
| M29 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (smooth) | 649.74 | 9.52 | 6.86e-03 | Smooth | Interaction only | Low |
| M43 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (smooth) | 650.12 | 9.89 | 5.68e-03 | Smooth | Main + Interaction | Low |
| M23 | Interaction: temp_max × wind_max_gust (smooth) | 650.17 | 9.95 | 5.53e-03 | Smooth | Interaction only | Low |
| M33 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (smooth) | 650.52 | 10.30 | 4.64e-03 | Smooth | Main + Interaction | Low |
| M39 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (smooth) | 651.39 | 11.17 | 3.00e-03 | Smooth | Main + Interaction | Low |
| M25 | Interaction: temp_max × sum_butterflies_direct_sun (smooth) | 651.78 | 11.56 | 2.47e-03 | Smooth | Interaction only | Low |
| M59 | Additive: temp_max + wind_max_gust (smooth) | 652.14 | 11.92 | 2.06e-03 | Smooth | Additive | Low |
| M55 | Additive: temp_min + temp_max (smooth) | 652.25 | 12.03 | 1.96e-03 | Smooth | Additive | Low |
| M15 | Interaction: temp_min × temp_at_max_count_t_1 (smooth) | 652.64 | 12.42 | 1.61e-03 | Smooth | Interaction only | Low |
| M17 | Interaction: temp_min × wind_max_gust (smooth) | 652.73 | 12.51 | 1.54e-03 | Smooth | Interaction only | Low |
| M11 | Single: sum_butterflies_direct_sun (smooth) | 652.82 | 12.60 | 1.47e-03 | Smooth | Single predictor | Low |
| M13 | Interaction: temp_min × temp_max (smooth) | 652.93 | 12.71 | 1.39e-03 | Smooth | Interaction only | Low |
| M1 | Null (smooth baseline) | 653.17 | 12.95 | 1.23e-03 | Smooth | Null | Low |
| M21 | Interaction: temp_max × temp_at_max_count_t_1 (smooth) | 653.48 | 13.26 | 1.06e-03 | Smooth | Interaction only | Low |
| M27 | Interaction: temp_at_max_count_t_1 × wind_max_gust (smooth) | 653.70 | 13.47 | 9.48e-04 | Smooth | Interaction only | Low |
| M49 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (smooth) | 653.88 | 13.66 | 8.66e-04 | Smooth | Main + Interaction | Low |
| M7 | Single: temp_at_max_count_t_1 (smooth) | 653.91 | 13.68 | 8.54e-04 | Smooth | Single predictor | Low |
| M52 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (linear) | 654.45 | 14.23 | 6.51e-04 | Linear | Main + Interaction | Low |
| M41 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (smooth) | 654.72 | 14.50 | 5.67e-04 | Smooth | Main + Interaction | Low |
| M3 | Single: temp_min (smooth) | 655.44 | 15.21 | 3.97e-04 | Smooth | Single predictor | Low |
| M9 | Single: wind_max_gust (smooth) | 655.52 | 15.30 | 3.81e-04 | Smooth | Single predictor | Low |
| M53 | Additive: All temperature (smooth) | 655.96 | 15.73 | 3.06e-04 | Smooth | Additive | Low |
| M67 | All temp + all temp interactions (smooth) | 656.75 | 16.53 | 2.06e-04 | Smooth | Complex | Moderate |
| M20 | Interaction: temp_min × sum_butterflies_direct_sun (linear) | 656.77 | 16.55 | 2.04e-04 | Linear | Interaction only | Low |
| M35 | Additive + Interaction: temp_min + temp_at_max_count_t_1 + temp_min×temp_at_max_count_t_1 (smooth) | 657.01 | 16.79 | 1.81e-04 | Smooth | Main + Interaction | Low |
| M61 | Additive: temp_at_max_count_t_1 + wind_max_gust (smooth) | 657.30 | 17.08 | 1.56e-04 | Smooth | Additive | Low |
| M57 | Additive: temp_min + wind_max_gust (smooth) | 657.68 | 17.46 | 1.29e-04 | Smooth | Additive | Low |
| M46 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (linear) | 657.70 | 17.47 | 1.28e-04 | Linear | Main + Interaction | Low |
| M30 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (linear) | 657.90 | 17.68 | 1.16e-04 | Linear | Interaction only | Low |
| M44 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (linear) | 658.01 | 17.79 | 1.10e-04 | Linear | Main + Interaction | Low |
| M6 | Single: temp_max (linear) | 658.09 | 17.87 | 1.05e-04 | Linear | Single predictor | Low |
| M47 | Additive + Interaction: temp_at_max_count_t_1 + wind_max_gust + temp_at_max_count_t_1×wind_max_gust (smooth) | 658.22 | 17.99 | 9.90e-05 | Smooth | Main + Interaction | Low |
| M24 | Interaction: temp_max × wind_max_gust (linear) | 658.24 | 18.02 | 9.77e-05 | Linear | Interaction only | Low |
| M40 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (linear) | 658.42 | 18.20 | 8.92e-05 | Linear | Main + Interaction | Low |
| M37 | Additive + Interaction: temp_min + wind_max_gust + temp_min×wind_max_gust (smooth) | 658.61 | 18.39 | 8.12e-05 | Smooth | Main + Interaction | Low |
| M34 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (linear) | 658.93 | 18.71 | 6.91e-05 | Linear | Main + Interaction | Low |
| M65 | Additive: All predictors (additive) (smooth) | 659.21 | 18.98 | 6.03e-05 | Smooth | Additive | Low |
| M63 | Additive: All temp + wind (smooth) | 659.30 | 19.07 | 5.76e-05 | Smooth | Additive | Low |
| M26 | Interaction: temp_max × sum_butterflies_direct_sun (linear) | 659.93 | 19.71 | 4.21e-05 | Linear | Interaction only | Low |
| M56 | Additive: temp_min + temp_max (linear) | 660.55 | 20.32 | 3.08e-05 | Linear | Additive | Low |
| M60 | Additive: temp_max + wind_max_gust (linear) | 660.76 | 20.54 | 2.77e-05 | Linear | Additive | Low |
| M16 | Interaction: temp_min × temp_at_max_count_t_1 (linear) | 660.78 | 20.55 | 2.75e-05 | Linear | Interaction only | Low |
| M18 | Interaction: temp_min × wind_max_gust (linear) | 661.01 | 20.79 | 2.44e-05 | Linear | Interaction only | Low |
| M14 | Interaction: temp_min × temp_max (linear) | 661.32 | 21.10 | 2.10e-05 | Linear | Interaction only | Low |
| M28 | Interaction: temp_at_max_count_t_1 × wind_max_gust (linear) | 661.49 | 21.27 | 1.92e-05 | Linear | Interaction only | Low |
| M2 | Null (linear baseline) | 661.63 | 21.41 | 1.79e-05 | Linear | Null | Low |
| M22 | Interaction: temp_max × temp_at_max_count_t_1 (linear) | 662.25 | 22.03 | 1.31e-05 | Linear | Interaction only | Low |
| M12 | Single: sum_butterflies_direct_sun (linear) | 662.35 | 22.13 | 1.25e-05 | Linear | Single predictor | Low |
| M42 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (linear) | 662.96 | 22.74 | 9.24e-06 | Linear | Main + Interaction | Low |
| M4 | Single: temp_min (linear) | 663.33 | 23.10 | 7.69e-06 | Linear | Single predictor | Low |
| M50 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (linear) | 663.53 | 23.31 | 6.93e-06 | Linear | Main + Interaction | Low |
| M54 | Additive: All temperature (linear) | 663.59 | 23.36 | 6.75e-06 | Linear | Additive | Low |
| M10 | Single: wind_max_gust (linear) | 663.79 | 23.57 | 6.09e-06 | Linear | Single predictor | Low |
| M69 | All additive + all temp×wind interactions (smooth) | 663.97 | 23.74 | 5.58e-06 | Smooth | Complex | Moderate |
| M8 | Single: temp_at_max_count_t_1 (linear) | 664.37 | 24.15 | 4.56e-06 | Linear | Single predictor | Low |
| M68 | All temp + all temp interactions (linear) | 664.52 | 24.30 | 4.23e-06 | Linear | Complex | Moderate |
| M58 | Additive: temp_min + wind_max_gust (linear) | 665.47 | 25.25 | 2.63e-06 | Linear | Additive | Low |
| M38 | Additive + Interaction: temp_min + wind_max_gust + temp_min×wind_max_gust (linear) | 666.02 | 25.80 | 1.99e-06 | Linear | Main + Interaction | Low |
| M36 | Additive + Interaction: temp_min + temp_at_max_count_t_1 + temp_min×temp_at_max_count_t_1 (linear) | 666.63 | 26.41 | 1.48e-06 | Linear | Main + Interaction | Low |
| M62 | Additive: temp_at_max_count_t_1 + wind_max_gust (linear) | 666.68 | 26.46 | 1.43e-06 | Linear | Additive | Low |
| M64 | Additive: All temp + wind (linear) | 666.83 | 26.61 | 1.33e-06 | Linear | Additive | Low |
| M48 | Additive + Interaction: temp_at_max_count_t_1 + wind_max_gust + temp_at_max_count_t_1×wind_max_gust (linear) | 666.96 | 26.73 | 1.25e-06 | Linear | Main + Interaction | Low |
| M66 | Additive: All predictors (additive) (linear) | 668.00 | 27.78 | 7.41e-07 | Linear | Additive | Low |
| M70 | All additive + all temp×wind interactions (linear) | 670.90 | 30.68 | 1.74e-07 | Linear | Complex | Moderate |
| M72 | FULL MODEL: All terms + all interactions (linear) | 710.96 | 70.74 | 3.49e-16 | Linear | Full model | High |
| M71 | FULL MODEL: All terms + all interactions (smooth) | 712.61 | 72.39 | 1.53e-16 | Smooth | Full model | High |
8.2 24-Hour Window: All 76 Models
| model | description | AICc | delta_AICc | weight_AICc | baseline_type | model_category | overfitting_risk |
|---|---|---|---|---|---|---|---|
| M31 | Interaction: wind_max_gust × sum_butterflies_direct_sun (smooth) | 636.33 | 0.00 | 5.07e-01 | Smooth | Interaction only | Low |
| M23 | Interaction: temp_max × wind_max_gust (smooth) | 639.92 | 3.59 | 8.44e-02 | Smooth | Interaction only | Low |
| M29 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (smooth) | 640.76 | 4.42 | 5.55e-02 | Smooth | Interaction only | Low |
| M19 | Interaction: temp_min × sum_butterflies_direct_sun (smooth) | 641.11 | 4.78 | 4.66e-02 | Smooth | Interaction only | Low |
| M51 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (smooth) | 641.72 | 5.39 | 3.42e-02 | Smooth | Main + Interaction | Low |
| M45 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (smooth) | 641.80 | 5.46 | 3.30e-02 | Smooth | Main + Interaction | Low |
| M5 | Single: temp_max (smooth) | 642.19 | 5.86 | 2.71e-02 | Smooth | Single predictor | Low |
| M67 | All temp + all temp interactions (smooth) | 642.49 | 6.16 | 2.33e-02 | Smooth | Complex | Moderate |
| M43 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (smooth) | 642.69 | 6.36 | 2.11e-02 | Smooth | Main + Interaction | Low |
| M17 | Interaction: temp_min × wind_max_gust (smooth) | 642.73 | 6.40 | 2.07e-02 | Smooth | Interaction only | Low |
| M25 | Interaction: temp_max × sum_butterflies_direct_sun (smooth) | 642.75 | 6.42 | 2.05e-02 | Smooth | Interaction only | Low |
| M33 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (smooth) | 642.90 | 6.57 | 1.90e-02 | Smooth | Main + Interaction | Low |
| M41 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (smooth) | 643.73 | 7.40 | 1.26e-02 | Smooth | Main + Interaction | Low |
| M15 | Interaction: temp_min × temp_at_max_count_t_1 (smooth) | 643.79 | 7.46 | 1.22e-02 | Smooth | Interaction only | Low |
| M32 | Interaction: wind_max_gust × sum_butterflies_direct_sun (linear) | 644.33 | 8.00 | 9.30e-03 | Linear | Interaction only | Low |
| M53 | Additive: All temperature (smooth) | 644.61 | 8.28 | 8.09e-03 | Smooth | Additive | Low |
| M27 | Interaction: temp_at_max_count_t_1 × wind_max_gust (smooth) | 644.95 | 8.62 | 6.82e-03 | Smooth | Interaction only | Low |
| M59 | Additive: temp_max + wind_max_gust (smooth) | 645.02 | 8.69 | 6.59e-03 | Smooth | Additive | Low |
| M55 | Additive: temp_min + temp_max (smooth) | 645.02 | 8.69 | 6.58e-03 | Smooth | Additive | Low |
| M21 | Interaction: temp_max × temp_at_max_count_t_1 (smooth) | 645.52 | 9.19 | 5.13e-03 | Smooth | Interaction only | Low |
| M1 | Null (smooth baseline) | 645.54 | 9.21 | 5.07e-03 | Smooth | Null | Low |
| M13 | Interaction: temp_min × temp_max (smooth) | 645.90 | 9.57 | 4.23e-03 | Smooth | Interaction only | Low |
| M39 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (smooth) | 646.00 | 9.66 | 4.04e-03 | Smooth | Main + Interaction | Low |
| M7 | Single: temp_at_max_count_t_1 (smooth) | 646.19 | 9.86 | 3.67e-03 | Smooth | Single predictor | Low |
| M49 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (smooth) | 646.79 | 10.46 | 2.72e-03 | Smooth | Main + Interaction | Low |
| M3 | Single: temp_min (smooth) | 647.30 | 10.97 | 2.10e-03 | Smooth | Single predictor | Low |
| M24 | Interaction: temp_max × wind_max_gust (linear) | 647.38 | 11.05 | 2.02e-03 | Linear | Interaction only | Low |
| M9 | Single: wind_max_gust (smooth) | 647.82 | 11.49 | 1.62e-03 | Smooth | Single predictor | Low |
| M11 | Single: sum_butterflies_direct_sun (smooth) | 648.02 | 11.69 | 1.47e-03 | Smooth | Single predictor | Low |
| M30 | Interaction: temp_at_max_count_t_1 × sum_butterflies_direct_sun (linear) | 648.22 | 11.89 | 1.33e-03 | Linear | Interaction only | Low |
| M35 | Additive + Interaction: temp_min + temp_at_max_count_t_1 + temp_min×temp_at_max_count_t_1 (smooth) | 648.40 | 12.06 | 1.22e-03 | Smooth | Main + Interaction | Low |
| M63 | Additive: All temp + wind (smooth) | 648.58 | 12.25 | 1.11e-03 | Smooth | Additive | Low |
| M20 | Interaction: temp_min × sum_butterflies_direct_sun (linear) | 648.79 | 12.46 | 9.98e-04 | Linear | Interaction only | Low |
| M68 | All temp + all temp interactions (linear) | 648.97 | 12.64 | 9.13e-04 | Linear | Complex | Moderate |
| M37 | Additive + Interaction: temp_min + wind_max_gust + temp_min×wind_max_gust (smooth) | 649.34 | 13.01 | 7.58e-04 | Smooth | Main + Interaction | Low |
| M61 | Additive: temp_at_max_count_t_1 + wind_max_gust (smooth) | 649.36 | 13.03 | 7.51e-04 | Smooth | Additive | Low |
| M47 | Additive + Interaction: temp_at_max_count_t_1 + wind_max_gust + temp_at_max_count_t_1×wind_max_gust (smooth) | 649.59 | 13.26 | 6.70e-04 | Smooth | Main + Interaction | Low |
| M52 | Additive + Interaction: wind_max_gust + sum_butterflies_direct_sun + wind_max_gust×sum_butterflies_direct_sun (linear) | 649.81 | 13.48 | 6.01e-04 | Linear | Main + Interaction | Low |
| M18 | Interaction: temp_min × wind_max_gust (linear) | 650.19 | 13.86 | 4.96e-04 | Linear | Interaction only | Low |
| M57 | Additive: temp_min + wind_max_gust (smooth) | 650.20 | 13.86 | 4.95e-04 | Smooth | Additive | Low |
| M26 | Interaction: temp_max × sum_butterflies_direct_sun (linear) | 650.34 | 14.01 | 4.61e-04 | Linear | Interaction only | Low |
| M44 | Additive + Interaction: temp_max + wind_max_gust + temp_max×wind_max_gust (linear) | 650.36 | 14.03 | 4.56e-04 | Linear | Main + Interaction | Low |
| M16 | Interaction: temp_min × temp_at_max_count_t_1 (linear) | 650.75 | 14.42 | 3.75e-04 | Linear | Interaction only | Low |
| M6 | Single: temp_max (linear) | 651.09 | 14.76 | 3.16e-04 | Linear | Single predictor | Low |
| M46 | Additive + Interaction: temp_max + sum_butterflies_direct_sun + temp_max×sum_butterflies_direct_sun (linear) | 651.41 | 15.08 | 2.70e-04 | Linear | Main + Interaction | Low |
| M42 | Additive + Interaction: temp_max + temp_at_max_count_t_1 + temp_max×temp_at_max_count_t_1 (linear) | 652.00 | 15.67 | 2.01e-04 | Linear | Main + Interaction | Low |
| M65 | Additive: All predictors (additive) (smooth) | 652.07 | 15.73 | 1.94e-04 | Smooth | Additive | Low |
| M28 | Interaction: temp_at_max_count_t_1 × wind_max_gust (linear) | 652.41 | 16.08 | 1.64e-04 | Linear | Interaction only | Low |
| M34 | Additive + Interaction: temp_min + temp_max + temp_min×temp_max (linear) | 652.81 | 16.48 | 1.34e-04 | Linear | Main + Interaction | Low |
| M22 | Interaction: temp_max × temp_at_max_count_t_1 (linear) | 652.98 | 16.65 | 1.23e-04 | Linear | Interaction only | Low |
| M2 | Null (linear baseline) | 653.04 | 16.71 | 1.20e-04 | Linear | Null | Low |
| M54 | Additive: All temperature (linear) | 653.07 | 16.74 | 1.17e-04 | Linear | Additive | Low |
| M14 | Interaction: temp_min × temp_max (linear) | 653.40 | 17.06 | 1.00e-04 | Linear | Interaction only | Low |
| M56 | Additive: temp_min + temp_max (linear) | 653.55 | 17.21 | 9.27e-05 | Linear | Additive | Low |
| M60 | Additive: temp_max + wind_max_gust (linear) | 653.72 | 17.39 | 8.51e-05 | Linear | Additive | Low |
| M40 | Additive + Interaction: temp_min + sum_butterflies_direct_sun + temp_min×sum_butterflies_direct_sun (linear) | 653.82 | 17.49 | 8.08e-05 | Linear | Main + Interaction | Low |
| M69 | All additive + all temp×wind interactions (smooth) | 654.00 | 17.67 | 7.39e-05 | Smooth | Complex | Moderate |
| M50 | Additive + Interaction: temp_at_max_count_t_1 + sum_butterflies_direct_sun + temp_at_max_count_t_1×sum_butterflies_direct_sun (linear) | 654.12 | 17.79 | 6.96e-05 | Linear | Main + Interaction | Low |
| M8 | Single: temp_at_max_count_t_1 (linear) | 654.78 | 18.45 | 5.01e-05 | Linear | Single predictor | Low |
| M4 | Single: temp_min (linear) | 654.82 | 18.49 | 4.90e-05 | Linear | Single predictor | Low |
| M10 | Single: wind_max_gust (linear) | 655.34 | 19.01 | 3.78e-05 | Linear | Single predictor | Low |
| M12 | Single: sum_butterflies_direct_sun (linear) | 655.95 | 19.62 | 2.78e-05 | Linear | Single predictor | Low |
| M36 | Additive + Interaction: temp_min + temp_at_max_count_t_1 + temp_min×temp_at_max_count_t_1 (linear) | 656.03 | 19.70 | 2.68e-05 | Linear | Main + Interaction | Low |
| M64 | Additive: All temp + wind (linear) | 656.48 | 20.15 | 2.14e-05 | Linear | Additive | Low |
| M38 | Additive + Interaction: temp_min + wind_max_gust + temp_min×wind_max_gust (linear) | 656.56 | 20.22 | 2.06e-05 | Linear | Main + Interaction | Low |
| M62 | Additive: temp_at_max_count_t_1 + wind_max_gust (linear) | 657.31 | 20.98 | 1.41e-05 | Linear | Additive | Low |
| M48 | Additive + Interaction: temp_at_max_count_t_1 + wind_max_gust + temp_at_max_count_t_1×wind_max_gust (linear) | 657.32 | 20.99 | 1.40e-05 | Linear | Main + Interaction | Low |
| M58 | Additive: temp_min + wind_max_gust (linear) | 657.60 | 21.27 | 1.22e-05 | Linear | Additive | Low |
| M66 | Additive: All predictors (additive) (linear) | 659.86 | 23.53 | 3.94e-06 | Linear | Additive | Low |
| M70 | All additive + all temp×wind interactions (linear) | 660.18 | 23.85 | 3.36e-06 | Linear | Complex | Moderate |
| M71 | FULL MODEL: All terms + all interactions (smooth) | 699.80 | 63.47 | 8.37e-15 | Smooth | Full model | High |
| M72 | FULL MODEL: All terms + all interactions (linear) | 703.91 | 67.58 | 1.07e-15 | Linear | Full model | High |
9 References
- Original analysis: Daily GAM Results
- Sunset window detailed analysis: sunset_window_gam_analysis.html
- 24-hour window detailed analysis: 24hr_window_gam_analysis.html
- Data sources:
data/monarch_daily_lag_analysis_sunset_window.csvdata/monarch_daily_lag_analysis_24hr_window.csv
Document generated: 2025-10-03